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arXiv · 1503.08740

Generalized Goldberg Formula

Antonio De Nicola·Ivan Yudin
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Abstract

In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed $p$-form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kaehler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a CDGA to the full de Rham algebra.

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Antonio De Nicola, Ivan Yudin. 2016-02-16. Generalized Goldberg Formula. https://doi.org/10.4153/cmb-2016-007-4

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